1.

Find the equation of the circle whose:(i) Centre (- 2, 3) and radius is 4(ii) Centre (a, b) and radius is a – b

Answer»

(i) According to question,

Centre of circle (h, k) = (- 2, 3)

and Radius of circle r = 4 unit

Then, equation of circle

From formula (x – h)2 + (y- k)2 = r2

[x – (- 2)]2 + (y – 3)2 = 42

⇒ (x + 2)2 + (y – 3)2 = 16

⇒ x2 + 4x + 4 + y2 – 6y + 9 = 16

⇒ x2 + y2 + 4x – 6y = 16 – 9 – 4

⇒ x2 + y2 + 4x – 6y = 3

⇒ x2 + y2 + 4x – 6y – 3 = 0

Thus, required equation of circle

x2 + y2 + 4x – 6y – 3 = 0.

(ii) According to question,

Centre of circle (h, k) = (a, b)

and Radius of circle r = (a – b) unit

Then, equation of circle
From formula (x – h)2 + (y – k)2 = r2

⇒ (x – a)2 + (y – b)2 = (a – b)2

⇒ x2 + a2 – 2ax + y2 + b2 – 2 by = a2 + b2 – 2ab

⇒ x2 + y2 – 2ax – 2by + a2 + b2 – a2 – b2 + 2ab = 0

⇒ x2 + y2 – ax – 2by + 2ab = 0.


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